Model-free analysis single field

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The Question

Is possible to use relax to perform a model-free analysis using only relaxation data collected at a single magnetic field strength?

The answer is yes!

The subject of single field strength data has been discussed numerous times on this mailing list. It is recommended to read previous responses to questions relating to single field strength data, and look the other messages in those threads. You will find these discussions quite informative and highly detailed:

  1. Danyun Zeng:
  2. Sean Leo Moro:
  3. Martin Ballaschk:
  4. Shantanu Bhattacharyya:
  5. Mengjun Xue:
  6. Fernando Amador:
  7. Shantanu Bhattacharyya:
  8. Dhanasekaran Muthu:
  9. Vitaly Vostrikov:
  10. Aldino Viegas:
  11. Pierre-Yves Savard:
  12. Keith Constantine:
  13. Clare-Louise Evans:
  14. Hongyan Li:

These will have lots of additional information. This is just a selection of possibly the most useful messages. You will soon see that this is a complicated topic. Note that relax is capable of performing 100% of the functionality of:

If you play with the optimisation settings you can even find identical results to within machine precision - relax can mimic these other softwares.


The key is that the full analysis protocol is rather complicated - many people don't understand this - and that these softwares do not implement the full iterative protocol. Therefore one either have to perform it manually or write a script to perform all of the steps.

The protocol is described in the relax manual in figure 7.2 (

In summary:

  1. Find an initial diffusion tensor estimate (you can do this in relax by only using model m0). This requires all non-mobile residues and side chain spins to be excluded, and this can be problematic. See the [d'Auvergne and Gooley, 2008b] paper for an example of the catastrophic failure that this initial estimate can result in. Or the bacteriorhodopsin fragment of [Orekhov et al., 1999] where this complete failure was earlier demonstrated.
  2. Optimise all of the model-free models from m0 to m9. This requires high precision optimisation, for a comparison of all the softwares see the [d'Auvergne and Gooley, 2008a] model-free optimisation paper. Only relax and DASHA implement the full range of model-free models, though the models m6, m7, and m8 cannot be used if only single field strength data is used (m6 is the original 2-time scale motion model of [Clore et al., 1990]).
  3. Eliminate failed models (this is only available in relax). See the [d'Auvergne and Gooley, 2006] model elimination paper.
  4. Select the best model-free model for each spin system. This again requires precision modern techniques, with the best being AIC model select (see the [d'Auvergne and Gooley, 2003] model-free model selection paper). If you are unaware that ANOVA statistics for model selection (hypothesis testing via chi-squared, F- and t-tests) was abandoned by the field of model selection over 100 years ago (a field which makes the NMR field look very, very small), then you should really look at that paper.
  5. Optimise the global model. This is the diffusion tensor plus the model-free models for all spin systems.
  6. Check for convergence (identical chi-squared values to a previous iteration, and not necessarily the last one). If no, then go back to b) and repeat. Note that the chi-squared value can go up significantly between iterations, but this is because the model is simplifying itself at a much faster rate by loosing parameters - it's Occam's razor at work. Again see the [d'Auvergne and Gooley, 2008b] paper for figures demonstrating this. The concept as to what is happening during this combined model-free optimisation and model selection algorithm is described in the [d'Auvergne and Gooley, 2007] paper. It can take up to 20 iterations or more to reach convergence, depending upon the quality of the relaxation data and the 3D structure or the system in study.
  7. Once steps a-f have been completed for all global models (characterised by the spheroid, prolate spheroid, oblate spheroid, and ellipsoid diffusion tensors), then model selection between the different global models needs to be performed.
  8. Monte Carlo simulations for error analysis must be performed at the end.
  9. Elimination of failed Monte Carlo simulations is essential for keeping the errors to reasonable values for certain spin systems. This is also a relax-only feature (see the [d'Auvergne and Gooley, 2007] model elimination paper).

These steps must be implemented independently of which software you use, as NONE implement the full protocol. Note however that the protocol I developed (in the [d'Auvergne and Gooley, 2007] theory paper and the [d'Auvergne and Gooley, 2008b] paper is fully implemented in relax, however this required multiple field strength data.

This is a rather large script located at auto_anlayses/ This protocol is used by the GUI. So one option would be to copy this auto_anlayses/ script and modify it for the figure 7.2 protocol.


I must warn you about using single field strength data. It is now quite difficult to publish a model-free analysis with only single field strength data as most of the field know about the catastrophic analysis failures resulting in large amounts of artificial motion. These failures can also be much more subtle. Many reviewers will ask for such data to be collected as the results cannot not be trusted otherwise. For a model-free analysis, it is almost essential to collect data at multiple field strengths, otherwise it can be sometimes impossible to distinguish between the anisotropic part of the Brownian tumbling of the molecule and internal motion - specifically due to the NH vectors in secondary structure elements all pointing in a similar direction. I have a much better explanation, as well as citations to all the relevant literature in [d'Auvergne and Gooley, 2007]. In this paper, you will see reviewed both the artificial nanosecond motions of the [Schurr et al., 1994] paper and the artifical Rex motions of the [Tjandra et al., 1995] paper.


Finally, you will probably find it much easier to spend the 7-8 days collecting data at another field strength than to implement the protocol in a relax, Modelfree4, or DASHA script (or via multiple iterations of the GUI programs), as well as study all of the relevant literature to understand all of the types of failures than only occurs with single field strength data. With multiple field strength data you can perform Sebastien Morin's consistency testing analysis in relax[Morin and Gagné, 2009] (see That way you can see if your per-experiment temperature calibration and per-experiment temperature control techniques have works sufficiently well ( and if you have used long enough recycle delays. Collecting data at a second field would probably save you significant amounts of time, and has the additional benefit that it would guarantee that the dynamics you see at the end will be real. I cannot emphasize enough how important it is to collect data at multiple fields, most importantly the NOE and R2 data.


  • [Clore et al., 1990] ^ Clore, G. M., Szabo, A., Bax, A., Kay, L. E., Driscoll, P. C., and Gronenborn, A. M. (1990). Deviations from the simple 2-parameter model-free approach to the interpretation of N-15 nuclear magnetic-relaxation of proteins. J. Am. Chem. Soc., 112(12), 4989-4991. (DOI: 10.1021/ja00168a070)
  • [d'Auvergne and Gooley, 2003] ^ d'Auvergne, E. J. and Gooley, P. R. (2003). The use of model selection in the model-free analysis of protein dynamics. J. Biomol. NMR, 25(1), 25-39. (DOI: 10.1023/a:1021902006114)
  • [d'Auvergne and Gooley, 2006] ^ d'Auvergne, E. J. and Gooley, P. R. (2006). Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data. J. Biomol. NMR, 35(2), 117-135. (DOI: 10.1007/s10858-006-9007-z)
  • [d'Auvergne and Gooley, 2007] ^ 1 2 3 4 d'Auvergne, E. J. and Gooley, P. R. (2007). Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm. Mol. BioSyst., 3(7), 483-494. (DOI: 10.1039/b702202f)
  • [d'Auvergne and Gooley, 2008a] ^ d'Auvergne, E. J. and Gooley, P. R. (2008). Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces. J. Biomol. NMR, 40(2), 107-119. (DOI: 10.1007/s10858-007-9214-2)
  • [d'Auvergne and Gooley, 2008b] ^ 1 2 3 d'Auvergne, E. J. and Gooley, P. R. (2008). Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor. J. Biomol. NMR, 40(2), 121-133. (DOI: 10.1007/s10858-007-9213-3)
  • [Morin and Gagné, 2009] ^ Morin, S. and Gagné, S. (2009). Simple tests for the validation of multiple field spin relaxation data. J. Biomol. NMR, 45, 361-372. (DOI: 10.1007/s10858-009-9381-4)
  • [Orekhov et al., 1999] ^ Orekhov, V. Y., Korzhnev, D. M., Diercks, T., Kessler, H., and Arseniev, A. S. (1999). H-1-N-15 NMR dynamic study of an isolated alpha-helical peptide (1-36)bacteriorhodopsin reveals the equilibrium helix-coil transitions. J. Biomol. NMR, 14(4), 345-356. (DOI: 10.1023/a:1008356809071)
  • [Schurr et al., 1994] ^ Schurr, J. M., Babcock, H. P., and Fujimoto, B. S. (1994). A test of the model-free formulas. Effects of anisotropic rotational diffusion and dimerization. J. Magn. Reson. B, 105(3), 211-224. (DOI: 10.1006/jmrb.1994.1127)
  • [Tjandra et al., 1995] ^ Tjandra, N., Wingfield, P., Stahl, S., and Bax, A. (1996). Anisotropic rotational diffusion of perdeuterated HIV protease from N-15 NMR relaxation measurements at two magnetic. J. Biomol. NMR, 8(3), 273-284. (DOI: 10.1007/bf00410326)

See also